The rate \(A_\oplus \)  may further be increased if we consider gravitational capture
of grains by interaction with giant planets in the Solar System.
Mainly low-velocity objects are captured and bound to the Solar System
by a cross section
\(\sigma _c (v) = \sigma _0 \, (v/v_c)^{-2} \, [ 1 + (v/v_c)^2]^{-2}\) ,
where \(\sigma _0 = 2.32 \times 10^5 \ \rm au^2\)  and \(v_c = 0.42\)  km/s [1]}.
A fraction \(f_\oplus \sim 10^{-4}\)  of the
captured objects are expected to hit Earth before they are lost from interplanetary space
[2]}, [1]}.
Then the accretion rate \(A_\oplus \)  is enhanced by a factor of
\(\eta _c = \langle \sigma _c v \rangle f_\oplus / (\pi r_\oplus ^2 \langle v \rangle )\sim 10^2\)  compared with direct hitting from ISM, and
thus \(A_\oplus \sim 1.6 \times 10^5 \,\eta _{c,2}\)  particles per year, where \(\eta _{c,2} \equiv \eta _c / 10^2\) . It should be noted
that the estimate of \(\eta _c\)  (especially \(f_\oplus \) ) is highly uncertain,
which is considering only
gravitational interactions. Radiative pressure and the PR drag effect may change
this estimate.
